based on the reference station, Sandy Hook, are shown to provide additional insight for the 

 errors involved in basing the tide probability estimates on reference stations rather than on 

 analyses of local tide records. At most stations, there is no alternative to basing tide 

 probability estimates on primary calculations at reference stations. At Atlantic City tlie 

 highest predicted high tides are a little higher and the lowest predicted high tides a httle 

 lower when the estimates are based on observations at Atlantic City tlian when based on 

 observations at Sandy Hook. For the table as a whole, however, the differences are not 

 large. 



Probability comparisons for other locations are presented in Appendix C by showing the 

 calculated distributions for reference stations as dashUnes on the graphs for the comparative 

 stations. The comparisons shown are Ukely to be more rehable than the average obtained 

 from applying the ranges in Appendix C to the probability calculations in Appendix B, since 

 all estimates of tidal range at these comparative stations were based on at least 29 days and 

 generally a fuU year of record. The selection of reference station and the estimation of tidal 

 range for many of the stations in Appendix C were generally based on less than 1 year of 

 record and sometimes on records shorter than 29 days. 



(1) Combined Probabilities of Astronomical Tide and Storm Effects on Sea Level. No 

 reasons are apparent for the assumption that the occurrence of storms is related to the phase 

 of the tide or tlie phase of the Moon. Although a given wind field will produce a steeper 

 slope on water surface in shallow water at low tide than at high tide, the effect varies with 

 the locahty and depends on the speed and direction of the wind over a large area and the 

 duration of the wind. The effect of tide stage on the contribution of tlie wind to the total 

 water level cannot generally be expressed as a function of tide stage alone. Therefore, it is 

 disregarded in the following discussion, since the astronomical tide and the storm surge are 

 considered independent variables. 



When the probability distribution functions are determined empirically (in Sec. Vll for 

 astronomical tides and by Myers (1970) for storm surges), the permissible values of the 

 variables may be the integers, 1, 2, 3, ... indicating the class numbers of the distribution 

 table. Computation of the probabUity function for the sum of two independent variables is 

 simple. Let p (k) be the probability that one variable is assigned to class k and Pj(k) be 

 the cumulative probability that the variable is not greater than k. Thus 



P^(k) = .|^ p^(k) (29) 



Let p (m) and P (m) be defined in a similar manner for a second variable. Let p (n) 



22 3 



and P (n) have similar definitions for the sum of the first and second variables. The prob- 



3 

 ability a given k will combine with a given m is given by 



79 



